   Chapter 11, Problem 23RE Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 1-32, find the derivative of the given function. f ( x ) = e x ( x 2 + 1 ) 10

To determine

To calculate: The derivative of the function f(x)=ex(x2+1)10.

Explanation

Given information:

The provided function is f(x)=ex(x2+1)10.

Formula used:

Product rule of derivative of differentiable functions, f(x) and g(x) is

ddx[f(x).g(x)]=f(x).g(x)+f(x).g(x).

The derivative of function f(x)=un using the chain rule is f(x)=ddx(un)=nun1dudx, where u is the function of x.

The derivative of e raised to x is ddxex=ex.

Calculation:

Consider the function,

f(x)=ex(x2+1)10

Apply product rule of derivative,

f(x)=ddxex(x2+1)10+exddx(x2+1)10

Apply the chain rule and simplify the derivative,

f(x)=ex(x2+1)10+ex10(x2+1)101ddx<

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